Finite Group Databasebeta

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C5×D3705 #49150334

order37050
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3705
unambiguous semidirect productC3⋊(C5×D1235)
unambiguous semidirect productC5⋊(C5×D741)
unambiguous semidirect productC13⋊(C5×D285)
unambiguous semidirect productC19⋊(C5×D195)

Splittings

Fitting, socle, HallC3×C52×C13×C19 ⋊ C2
derivedC3×C5×C13×C19 ⋊ C2×C5
HallC52×C13×C19 ⋊ D3
HallC3×C52×C19 ⋊ D13
HallC3×C52×C13 ⋊ D19
HallC3×C13×C19 ⋊ C5×D5
HallC52×C19 ⋊ D39
HallC52×C13 ⋊ D57
HallC13×C19 ⋊ C5×D15
HallC3×C52 ⋊ D247
HallC3×C19 ⋊ C5×D65
HallC3×C13 ⋊ C5×D95
SylowC52 ⋊ D741
SylowC19 ⋊ C5×D195
SylowC13 ⋊ C5×D285
SylowC3 ⋊ C5×D1235

Subgroups

subgroupG/H
center, hypercenterC5D3705
commutator, cosocle, hypocenterC3×C5×C13×C19C2×C5
FrattiniC1G
Fitting, socleC3×C52×C13×C19C2
LCSG ▷ C3×C5×C13×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7410

Conjugacy classes & character table

9270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 160);